Finite Group Databasebeta

← #14651474

Subgroups — #14651474

Order 2816.

432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077700C211yesmaximal, characteristic
2#13073832C211yesmaximal, characteristic
3#13067333C211yesmaximal, characteristic
4#13066959C211yesmaximal, characteristic
5#13066473C211yesmaximal, characteristic
6#13066471C211yesmaximal, characteristic
7C11×#1556C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12#10622843—21no—
13#10622843—21no—
14#10622595—21no—
15#10622595—21no—
16#10622590C412yes—
17#10622587C412yes—
18C4×C4⋊Dic11C2211yescharacteristic
19#10622539C2211yescharacteristic
20#10622539C2211yescharacteristic
21#10622441—22no—
22#10622332—21no—
23#10622331—21no—
24#10622314—22no—
25C11×#332—22no—
26#10622185—22no—
27#10622107—21no—
28#10622107—21no—
29C22×Q8×C11—21no—
30C22×Dic22C2×C411yescharacteristic
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C412yes—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×Dic11⋊C4D411yescharacteristic
41C2×Dic11⋊C4D411yescharacteristic
42C2×C4×Dic11C2×C412yes—
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C4×Dic22—21no—
48C4×Dic22—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#97—21no—
54C11×#97—21no—
55C11⋊#95—21no—
56C11⋊#95—22no—
57C11⋊#95—22no—
58C11⋊#95—22no—
59C11⋊#95—22no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66879—22no—
63Dic11⋊C8—22no—
64Dic11⋊C8—22no—
65C8×Dic11—22no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68#66867—21no—
69#66867—21no—
70#9456—111nomaximal, Sylow
71C2×Q8×C11—44no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C22×C4×C11—22no—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×Dic11—22no—
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C2×Dic22—22no—
84C2×Dic22—21no—
85C2×Dic22—21no—
86C2×Dic22—41no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—42no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—42no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111#2983—111no—
112#2568—111no—
113#1556—111no—
114#1556D1111yescharacteristic
115#1467—111no—
116#1285—111no—
117#1285—111no—
118C23×C11C2×C22⋊C411yescharacteristic
119Q8×C11—82no—
120Q8×C11—82no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—41no—
125C2×C4×C11—44no—
126C2×C4×C11—42no—
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11#10112yes—
146Dic22—42no—
147Dic22—42no—
148C8×C11—42no—
149C8×C11—81no—
150C11⋊C8—42no—
151C11⋊C8—81no—
152C2×C4⋊Q8C2×D1111yescharacteristic
153C2×C4×Q8—111no—
154#446—222no—
155#446—222no—
156#432—111no—
157#432—111no—
158#432—221no—
159#432C2×D1111yescharacteristic
160#432C2×D1111yescharacteristic
161#431—221no—
162#400—221no—
163#400—221no—
164#391—112no—
165#391—221no—
166#391—221no—
167#382—112no—
168C4×C4⋊C4—111no—
169#332—22no—
170#332—222no—
171#324—221no—
172#324—221no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#38611yescharacteristic
176C22×C11C2×#10111yescharacteristic
177C22×C11#41311yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—82no—
184C4×C11#45412yes—
185Dic11—22no—
186Dic11—41no—
187Dic11—41no—
188Dic11—41no—
189Dic11—82no—
190C22×Q8—21no—
191C22×Q8—111no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4×Q8—221no—
197C4×Q8—221no—
198C4×Q8—221no—
199C4×Q8—221no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4C4×D1112yes—
206C2×C42—111no—
207C2×C42—111no—
208C2×C42—112no—
209C2×C42C22×D1111yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—112no—
212C4⋊C8—222no—
213C4⋊C8—222no—
214C4⋊C8—221no—
215C4⋊C8C22⋊D1112yes—
216C22⋊C8—21no—
217C22⋊C8—21no—
218C22⋊C8—221no—
219C22⋊C8—221no—
220#97—21no—
221#97—21no—
222#97—222no—
223#97—221no—
224#97—221no—
225C4×C8—222no—
226#95—222no—
227#95—222no—
228#95—222no—
229#95—222no—
230#95—221no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#188811yescharacteristic
234C2×C11#190111yescharacteristic
235C2×C11#190911yescharacteristic
236C2×Q8—44no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—222no—
240C2×Q8—221no—
241C2×Q8—221no—
242C2×Q8—441no—
243C22×C4—22no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—222no—
249C22×C4C2×C4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251C22×C4D4×D1111yescharacteristic
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—222no—
255C2×C8—441no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—442no—
267C42—221no—
268C42—221no—
269C42—221no—
270C42—221no—
271C42—442no—
272C42#433911yescharacteristic
273C42D4×D1111yescharacteristic
274C42#434111yescharacteristic
275C42C2×C22⋊D1111yescharacteristic
276C11#945611yescharacteristic, complemented, Sylow
277C23C22⋊C4×D1111yescharacteristic
278Q8—82no—
279Q8—82no—
280Q8—442no—
281Q8—442no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—112no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4(C22⋊D11)⋊C411yescharacteristic
302C2×C4#6693611yescharacteristic
303C2×C4#6693711yescharacteristic
304C2×C4C4×C22⋊D1111yescharacteristic
305C2×C4#6699011yescharacteristic
306C2×C4#6699111yescharacteristic
307C8—42no—
308C8—81no—
309C8—442no—
310C8—881no—
311C22—21no—
312C22—21no—
313C22D11×#10111yescharacteristic
314C22#1062236411yescharacteristic
315C22#1062256911yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—222no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4—882no—
327C4#1062281412yes—
328C2—21no—
329C2—21no—
330C2#1306901611yescharacteristic
331C2#1306908111yescharacteristic
332C2#1306913511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1556C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1556D11
hypocenterC11#9456
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
276. C11#9456semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130777002
#130738322
#130673332
#130669592
#130664732
#130664712
C11×#15562
#945611